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Free Vibrations of a Nonlinearly Deformable Isotropic on the Average Composite Rectangular Membrane

A refined vibration equation of a rectangular membrane is derived in this paper. It allows determining the natural frequencies as functions of the mechanical characteristics of an asymmetrically stretched membrane. The dynamic equation is generalized to the case of a nonlinearly deformable isotropic...

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Bibliographic Details
Published in:Mechanics of composite materials 2018-03, Vol.54 (1), p.79-88
Main Authors: Tarasyuk, I. A., Kravchuk, A. S., Mikhasev, G. I.
Format: Article
Language:English
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Summary:A refined vibration equation of a rectangular membrane is derived in this paper. It allows determining the natural frequencies as functions of the mechanical characteristics of an asymmetrically stretched membrane. The dynamic equation is generalized to the case of a nonlinearly deformable isotropic on the average composite material. An approximate analytical solution of the problem is found employing a new homogenization technique. This method is based on estimation of the effective deformation characteristics of the composite material. The range of its effective characteristics is obtained from the rule of mixtures for the stresses and strains found assuming Voigt and Reuss hypotheses. The nonlinear behavior of the material is modeled using the bilinear Prandtl diagrams as constitutive equations for components of the composite. The effective elastic moduli, hardening modulus, yield stress, and the natural frequencies as functions of elastoplastic characteristics of the composite are obtained analytically in a closed form.
ISSN:0191-5665
1573-8922
DOI:10.1007/s11029-018-9720-1